List of top Questions asked in GATE NM- 2022

In a vapour compression refrigeration cycle using R134a, the enthalpies are (i) 240 kJ/kg at the beginning of compression, (ii) 275 kJ/kg at the end of compression, (iii) 96 kJ/kg at the beginning of throttling. Then the coefficient of performance (COP) of the cycle is ____________ (rounded off to one decimal place).

A steady incompressible laminar flow exists between two long parallel plates separated by \(h = 1\ \text{m}\). The bottom plate is fixed and the upper plate moves with velocity \(U = 10\ \text{m/s}\). The kinematic viscosity of the fluid is \(10^{-6}\ \text{m}^2/\text{s}\) and density is \(10^3\ \text{kg/m}^3\). No pressure gradient acts. Then the shear stress at the bottom plate is ____________ N/m\(^2\) (correct to two decimal places).

Consider a steady flow through a horizontal nozzle. The nozzle inlet area is 1 m\(^2\) and the outlet area is 0.05 m\(^2\). At the outlet, the flow discharges to atmosphere. Assuming the flow to be incompressible and frictionless, and the density of the fluid as 1 kg/m\(^3\), the gauge pressure required at the nozzle inlet to produce an outlet speed of 100 m/s is ________________ N/m\(^2\) (rounded off to nearest integer).

A rectangular barge has length (L) of 100 m, breadth (B) of 18 m and depth (D) of 10 m. It is subdivided transversely into four equal compartments of equal length with the end compartments loaded fully with oil of density = 0.9 tonne/m\(^3\). The barge floats in water having a density of 1000 kg/m\(^3\). If the hull structural weight is ignored, then the transverse metacentric height of the barge is ______________ m (correct to two decimal places).

A propeller rotating at a speed of 108 RPM behind the ship produces a thrust of 720 kN with a torque of 700 kNm, when it travels at a speed of 15 knots. In open water, this propeller rotating at the same speed, produces the same thrust at an advance speed of 12 knots, and develops the same torque at an advance speed of 12.3 knots. Then, the average of the wake fractions is ____________ (correct to two decimal places).

Consider a point source in a uniform flow of velocity \(U = 4\) m/s along the positive \(x\)-axis as shown in the figure. Assume a two-dimensional steady potential flow. The potential due to the point source is given by \(\log_e(r)\), where \(r^2 = x^2 + y^2\). Then the magnitude of the distance \(d\) between the point source and the stagnation point is ________________ m (rounded off to two decimal places).

Consider a ship with one half of its midship cross-section with moulded breadth \(B = 30\ \text{m}\) and moulded depth \(D = 9\ \text{m}\). The deck, side-shell, and bottom plate have the same thickness. The yield stress of the material is \(240\ \text{MPa}\). The section is subjected to a vertical bending moment of \(712.8\ \text{MN·m}\). Ignore the self-moment of inertia of deck and bottom plating. The distance of the farthest fiber from the neutral axis is taken excluding plate thickness. If maximum bending stress equals yield stress, the required plate thickness is ____________ mm (rounded off to one decimal place).

A ship moves at \(U = 9.81\ \text{m/s}\) in deep water. A wave is incident at an angle \(\beta = 120^\circ\). The encounter period measured onboard is \(4.187\ \text{s}\). Using \(g = 9.81\ \text{m/s}^2\), determine the actual wave period ____________ s (rounded off to one decimal place).

An air standard Otto cycle has a compression ratio of 6 and a mean effective pressure of 1000 kPa. Assume that the specific heat ratio \(\gamma\) is 1.4 and specific gas constant \(R\) as 0.287 kJ/kgK for the air. If the pressure and temperature at the beginning of the compression stroke are 100 kPa and 300 K, respectively, then the specific work output of the cycle is ________________ kJ/kg (rounded off to one decimal place).

If methane (CH\(_4\)) gas reacts with air at a stoichiometric proportion, then the air–fuel ratio of the combustion process is ________________ (rounded off to one decimal place).

Which of the following statements are TRUE for a fluid flow over a deeply submerged body?

For an Otto cycle with compression ratio $r$ and specific heat ratio $\gamma$, which expression represents the thermal efficiency?

Let \(y(x)\) be the solution of the differential equation \(y'' - 4y' - 12y = 3e^{5x}\) satisfying \(y(0)=\frac{18{7}\) and \(y'(0)=-\frac{1}{7}\). Then \(y(1)\) is ______________ (rounded off to nearest integer).}

We have two coins. One is biased with probability of head = 1.0 and the other is a fair coin. One coin is chosen at random and tossed twice. If both outcomes are heads, the probability that the chosen coin is fair is ____________ (correct to one decimal place).

An element, as shown in the figure, is subjected to stresses \(\sigma_x = 500\ \text{N/m}^2\), \(\sigma_y = 300\ \text{N/m}^2\) and \(\tau = 120\ \text{N/m}^2\). If \(\sigma_1\) and \(\sigma_2\) are the principal stresses, then the absolute value of the angle \(\varphi\) is ________________ degree (rounded off to one decimal place).

An under-damped single-degree-of-freedom system is freely oscillating with an initial amplitude \(A\). The initial velocity is zero. After five cycles of oscillation, the amplitude reduces to \(A/2\). Then the damping ratio of the system is ________________ % (rounded off to one decimal place) of critical damping.

A system with two degrees of freedom, as shown in the figure, has masses \(m_1 = 200\ \text{kg}\) and \(m_2 = 100\ \text{kg}\) and stiffness coefficients \(k_1 = k_2 = 200\ \text{N/m}\). Then the lowest natural frequency of the system is ____________ rad/s (rounded off to one decimal place).

A horizontal cylinder of 1.0 m diameter is placed transversely at the aft of a ship and is completely immersed in water. The cylinder rotates at 100 RPM and inflow velocity is 10 m/s. Water density is 1000 kg/m\(^3\). Assuming an ideal planar flow, the lift force per unit length acting on the cylinder is ____________ kN/m (rounded off to one decimal place).

Let \[ M = \begin{pmatrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{pmatrix} \] Which of the following are TRUE?

Which of the following statements are TRUE about the assumptions adopted in Euler’s column theory?

An autonomous underwater vehicle is made of a long cylinder with a semi-ellipsoid at the forward end and a hemisphere at the aft end as shown in the figure. The origin of the reference frame is located at the centroid of the cylinder.
The positive x, y and z axes, respectively, are pointing towards forward, port and upward directions. The surge, sway and heave motions are represented by indices 1-2-3 and roll, pitch and yaw motions are represented by indices 4-5-6, respectively.
If A = [A\(_{ij}\)] is the added mass matrix, then which of the following are NOT zero?

If a ship hull is subdivided into different watertight compartments, which of the following statements are TRUE?

Consider the midship section of a vessel with the centerline (CL) and neutral axis (NA) as shown in the figure. Assume that the cross-section is symmetric about the centerline, the plate thickness is uniform throughout the section and \(h_1<h_2\). When the vessel is subjected to a vertical bending moment in its upright condition, which of the following statements are TRUE?

For a simple vapour compression refrigeration, which of the following thermodynamic cycles (1-2-3-4) are possible? Here, \( T \), \( P \), \( S \), and \( h \) indicate temperature, pressure, specific entropy, and specific enthalpy, respectively.

The value of the line integral \[ \oint_{C} (-3y\,dx + 3x\,dy + z\,dz) \] along the circle \( C: x^{2} + y^{2} = 1,\ z = 1 \) oriented in the clockwise sense as seen from the origin, is